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Maths Mindset

Productive struggle in maths

Give problems that are challenging but still reachable with support.

Quick answer

Productive struggle in maths means working on problems that are hard enough to make you think, but not so hard that you give up. It’s about trying, making mistakes, and learning from them to get better at maths.

Learning outcome

By the end of this page, you will understand what productive struggle in maths means and how it helps you learn better. Success signs:
  • You can explain why it's good to try hard problems
  • You know how to ask for help when you're stuck
  • You feel proud when you solve a problem after trying hard
  • You understand that making mistakes is part of learning

Why this matters

Productive struggle is like a puzzle that's just tricky enough to make you think. It helps your brain grow stronger, just like how exercise helps your muscles grow. When you try hard problems, you learn more than if you just get the answers right away. It helps you become a better problem solver and makes maths more fun because you feel proud when you work through something difficult. Think of it like learning to ride a bike. At first, you might fall down, but you keep trying, and soon you can ride without falling. That’s productive struggle in action.

How it works

Productive struggle is not about failing or feeling bad. It's about:
  1. Trying a problem that's a bit hard
  2. Working through it, even if you don’t get it right away
  3. Asking for help or trying a different way if you get stuck
  4. Learning from your mistakes
  5. Feeling proud when you solve it
Let’s say you’re learning to multiply. If you just memorise 5 x 6 = 30, you might not understand what it means. But if you try to figure out 5 x 6 by adding 5 six times (5 + 5 + 5 + 5 + 5 + 5), you understand the idea better. That’s productive struggle.

Examples you can see

Let’s try a fun example together. Imagine you have 3 boxes, and each box has 4 toy cars inside. How many toy cars do you have in total? Step 1: You can think of this as 3 groups of 4 cars. Step 2: You can add them up: 4 + 4 + 4 = 12. Step 3: You can also multiply: 3 x 4 = 12. Now let’s try something a bit trickier. What if you have 6 boxes, and each box has 5 toy cars? How many cars do you have? Step 1: You can think of 6 groups of 5 cars. Step 2: Add them up: 5 + 5 + 5 + 5 + 5 + 5 = 30. Step 3: Multiply: 6 x 5 = 30. This is a great way to learn because you’re thinking hard and using what you know to figure out something new. Here’s another example from real life. You're helping your mum bake cookies. The recipe says you need 2 cups of flour for every 12 cookies. You want to make 24 cookies. How much flour do you need? Step 1: You know that 2 cups = 12 cookies. Step 2: You can double it: 2 + 2 = 4 cups for 24 cookies. Step 3: You can also think: 24 ÷ 12 = 2 groups, so 2 x 2 = 4 cups. This shows how maths helps you in the kitchen, and how you can solve problems by thinking carefully.

Try it as a mini adventure

Adventure: The Treasure Hunt You’re on a treasure hunt with your friends. You need to solve a riddle to find the treasure. The riddle says: “I have 5 bags. Each bag has 6 gold coins. How many coins do I have in total?” Step 1: Think about how many groups of coins you have. Step 2: Add them up: 6 + 6 + 6 + 6 + 6 = ? Step 3: Try multiplying: 5 x 6 = ? Step 4: You can draw 5 bags and put 6 coins in each to help you count. If you get stuck, ask a friend or a grown-up for help. It’s okay to need help when the problem is hard. Another challenge: You have 7 toy robots, and each robot has 3 wheels. How many wheels do you have in total? Step 1: Think: 7 groups of 3 wheels. Step 2: Add: 3 + 3 + 3 + 3 + 3 + 3 + 3 = ? Step 3: Multiply: 7 x 3 = ? This is a fun way to think about multiplication and practice your problem-solving skills.

Common mistakes

  • Mistake: Giving up when a problem is hard. Why it happens: It can feel frustrating or scary. Fix: Try one step at a time, and ask for help if you need it.
  • Mistake: Thinking that getting the answer right the first time is the only way to be good at maths. Why it happens: Some people think that if they don’t know it right away, they’re not smart. Fix: Making mistakes is normal and helps you learn more.
  • Mistake: Not trying to solve a problem by yourself before asking for help. Why it happens: You might feel lazy or want to be quick. Fix: Try your best first, then ask for help if you still need it.
  • Mistake: Not celebrating when you solve a hard problem. Why it happens: You might not feel proud of the effort. Fix: Remember that trying hard is just as important as getting the right answer.

Parent and carer guide

As a parent or carer, you can help your child with productive struggle by:
  • Encouraging them to try problems, even if they’re hard
  • Letting them make mistakes and learn from them
  • Helping them ask for help when needed
  • Not solving the problem for them, but asking questions like: “What do you think you should try next?”
  • Praising effort, not just results
  • Making sure they know it’s okay to feel confused or frustrated sometimes
  • Using everyday situations to practice maths, like cooking or shopping
You can also say things like:
  • “That’s a hard one, but you’re trying your best!”
  • “It’s okay to not know the answer right away.”
  • “Let’s look at this together.”
  • “You’re learning so much by working hard.”
Remember, your child’s brain is growing every time they try a hard problem and keep going.

Practice questions

  1. How many wheels are there on 4 toy cars if each car has 4 wheels?
  2. If you have 8 boxes and each box has 3 apples, how many apples are there?
  3. You have 5 bags with 7 marbles in each. How many marbles do you have?
  4. How many legs do 6 spiders have if each spider has 8 legs?
  5. If you have 9 toy animals and each animal has 2 ears, how many ears do you have?
Answers:
  1. 4 x 4 = 16 wheels
  2. 8 x 3 = 24 apples
  3. 5 x 7 = 35 marbles
  4. 6 x 8 = 48 legs
  5. 9 x 2 = 18 ears

FAQ

What is productive struggle in maths?

Productive struggle means trying to solve problems that are hard but still possible with effort and help. It’s not about giving up, but about learning and growing by thinking hard.

Why is it important to struggle with maths?

When you struggle with a problem, your brain grows stronger. It helps you understand maths better and makes you more confident in solving new problems.

What should I do when I get stuck on a maths problem?

Try one step at a time, draw a picture, ask a friend or grown-up for help, or break the problem into smaller parts.

Is it okay to make mistakes in maths?

Yes! Making mistakes is part of learning. It helps you understand what to do next and makes you better at maths.

How can I help my child with productive struggle?

Support them by encouraging effort, asking questions, letting them try, and praising their hard work, not just the right answers.